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Non-linear Fokker-Planck equations from conformal metrics and scalar curvature

Nov 15, 2019
23 pages
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Abstract: (arXiv)
We present an argument which intends to explore a potential geometric origin of a class of non-linear Fokker-Planck equations related to the mesoscopic behavior of systems conjecturally described by the qq-entropy. We argue that the appearance of the non-linear term(s) in such equations can be ascribed to the fact that the effective mesoscopic metric describing the behavior of the underlying system may not be the originally chosen one, but a conformal deformation of it. Motivated by Liouville's theorem, we highlight the role played by the scalar curvature of conformally related metrics in establishing such a non-linear Fokker-Planck equation.
Note:
  • 23 pages. No figures. LaTeX2e
  • q-entropy
  • Tsallis entropy
  • Fokker-Planck equation
  • Nonextensive statistics
  • Nonadditive entropy
  • Scalar curvature
  • curvature: scalar
  • deformation: conformal
  • entropy: Tsallis
  • nonlinear
  • [1]
    Stochastic Processes in Physics and Chemistry, 3rd Ed / Amsterdam, The Netherlands . 17
    • N. van Kampen
  • [2]
    The Fokker-Planck Equation: Methods of Solution and Applications, 2nd Ed / -Verlag, Berlin, Germany
    • H. Risken
  • [3]
    Nonlinear Fokker-Planck Equations: Fundamentals and Applications, SpringerVerlag, Berlin, Germany
    • T.D. Frank
  • [4]
    Introduction to Nonextensive Statistical Mechanics: Approaching a Complex World / Science + Business Media, New York, NY, USA
    • C. Tsallis
  • [5]
    Non-extensive statistical mechanics and generalized Fokker-Planck equation
    • A.R. Plastino
      ,
    • A. Plastino
      • Physica A 222 (1995) 347-354
  • [6]
    Anomalous diffusion in the presence of external sources: Exact time-dependent solutions and their thermostatistical basis
    • C. Tsallis
      ,
    • D.J. Bukman
      • Phys.Rev.E 54 (1996) R2197-R2200
  • [8]
    The nonlinear Fokker-Planck equation with state dependent diffusion-a nonextensive maximum entropy approach
    • L. Borland
      ,
    • F. Penini
      ,
    • A.R. Plastino
      ,
    • A. Plastino
      • Eur.Phys.J.B 12 (1998) 285-297
  • [10]
    Free energies based on generalized entropies and H-theorems for nonlinear FokkerPlanck equations
    • M. Shiino
      • J.Math.Phys. 42 (2001) 2540
  • [12]
    N-dimensional nonlinear FokkerPlanck equation wih time-dependent coefficients
    • L.C. Malacarne
      ,
    • R.S. Mendes
      ,
    • I.T. Pedron
      ,
    • E.K. Lenzi
      • Phys.Rev.E 65 (2002) 052101
  • [13]
    Generalized Fokker-Planck equations derived from generalized linear nonequlibrium thermodynamics
    • T.D. Frank
      • Physica A 310 (2002) 397-412
  • [14]
    Derivation of nonlinear Fokker-Planck equations by means of approximations to the master equation / 18
    • E.M.F. Curado
      ,
    • F.D. Nobre
      • Phys.Rev.E 67 (2003) 021107
  • [15]
    Generalized Fokker-Planck equations and effective thermodynamics
    • P.-H. Chavanis
      • Physica A 340 (2004) 57-65
  • [16]
    A procedure for obtaining general nonlinear Fokker-Planck equations
    • F.D. Nobre
      ,
    • E.M.F. Curado
      ,
    • G. Rowlands
      • Physica A 334 (2004) 109-118
  • [17]
    A general nonlinear Fokker-Planck equation and its associated entropy
    • V. Schwämmle
      ,
    • E.M.F. Curado
      ,
    • F.D. Nobre
      • Eur.Phys.J.B 58 (2007) 159-165
  • [18]
    q-Gaussians in the porous-medium equation: stability and time evolution
    • V. Schwämmle
      ,
    • F.D. Nobre
      ,
    • C. Tsallis
      • Eur.Phys.J.B 66 (2008) 537-546
  • [19]
    Computing the nonlinear anomalous diffusion equation from first principles
    • M.A. Fuentes
      ,
    • M.O. Cáceres
      • Phys.Lett.A 372 (2008) 1236-1239
  • [20]
    Dynamics of normal and anomalous diffusion in nonlinear Fokker-Planck equations
    • V. Schwämmle
      ,
    • E.M.F. Curado
      ,
    • F.D. Nobre
      • Eur.Phys.J.B 70 (2009) 107-116
  • [21]
    Thermostatistics of overdamped motion of interacting particles
    • J.S. Andrade
      ,
    • Jr.
      ,
    • G.F.T. da Silva
      ,
    • A.A. Moreira
      ,
    • F.D. Nobre
    et al.
      • Phys.Rev.Lett. 105 (2010) 260601
  • [22]
    Nonlinear Fokker-Planck Equations Associated with Genralized Entropies: Dynamical Characterization and Stability Analyses
    • M. Shiino
      • J.Phys.Conf.Ser. 201 (2010) 012004
  • [23]
    Classes of N-Dimensional Nonlinear / FokkerPlanck Equations Associated to Tsallis Entropy
    • M.S. Ribeiro
      ,
    • F.D. Nobre
      ,
    • E.M.F. Curado
      • Entropy 13 (2011) 1928-1944
  • [24]
    JP Boon, Microscopic theory of anomalous diffusion based on particle interactions
    • J.F. Lutsko
      • Phys.Rev.E 88 (2013) 022108
  • [25]
    Nonlinear inhomogeneous Fokker-Planck equation within a generalized Stratonovich prescription
    • Z.G. Arenas
      ,
    • D.G. Barci
      ,
    • C. Tsallis
      • Phys.Rev.E 90 (2014) 032118
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